Chemical Thermodynamics for Process Simulation E-Book

Jürgen Gmehling

• Herausgeber: Wiley-VCH Verlag GmbH & Co. KGaA
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 1061

Veröffentlichungsjahr: 2019

Beschreibung

The only textbook that applies thermodynamics to real-world process engineering problems

This must-read for advanced students and professionals alike is the first book to demonstrate how chemical thermodynamics work in the real world by applying them to actual engineering examples. It also discusses the advantages and disadvantages of the particular models and procedures, and explains the most important models that are applied in process industry. All the topics are illustrated with examples that are closely related to practical process simulation problems. At the end of each chapter, additional calculation examples are given to enable readers to extend their comprehension.

Chemical Thermodynamics for Process Simulation instructs on the behavior of fluids for pure fluids, describing the main types of equations of state and their abilities. It discusses the various quantities of interest in process simulation, their correlation, and prediction in detail. Chapters look at the important terms for the description of the thermodynamics of mixtures; the most important models and routes for phase equilibrium calculation; models which are applicable to a wide variety of non-electrolyte systems; membrane processes; polymer thermodynamics; enthalpy of reaction; chemical equilibria, and more.

-Explains thermodynamic fundamentals used in process simulation with solved examples
-Includes new chapters about modern measurement techniques, retrograde condensation, and simultaneous description of chemical equilibrium
-Comprises numerous solved examples, which simplify the understanding of the often complex calculation procedures, and discusses advantages and disadvantages of models and procedures
-Includes estimation methods for thermophysical properties and phase equilibria thermodynamics of alternative separation processes
-Supplemented with MathCAD-sheets and DDBST programs for readers to reproduce the examples

Chemical Thermodynamics for Process Simulation is an ideal resource for those working in the fields of process development, process synthesis, or process optimization, and an excellent book for students in the engineering sciences.

Leseprobe

Table of Contents

Cover

Preface

Preface to the Second Edition

List of Symbols

Greek Symbols

Special symbols

Subscripts

Superscripts

Mathematics

Conversion factors

About the Authors

1 Introduction

2

PvT

Behavior of Pure Components

2.1 General Description

2.2 Caloric Properties

2.3 Ideal Gases

2.4 Real Fluids

2.5 Equations of State

Problems

References

3 Correlation and Estimation of Pure Component Properties

3.1 Introduction

3.2 Characteristic Physical Property Constants

3.3 Temperature‐Dependent Properties

3.4 Correlation and Estimation of Transport Properties

References

4 Properties of Mixtures

4.1 Introduction

4.2 Property Changes of Mixing

4.3 Partial Molar Properties

4.4 Gibbs–Duhem Equation

4.5 Ideal Mixture of Ideal Gases

4.6 Ideal Mixture of Real Fluids

4.7 Excess Properties

4.8 Fugacity in Mixtures

4.9 Activity and Activity Coefficient

4.10 Application of Equations of State to Mixtures

References

5 Phase Equilibria in Fluid Systems

5.1 Introduction

5.2 Thermodynamic Fundamentals

5.3 Application of Activity Coefficients

5.4 Calculation of Vapor–Liquid Equilibria Using

g

Models

5.5 Fitting of

g

Model Parameters

5.6 Calculation of Vapor–Liquid Equilibria Using Equations of State

5.7 Conditions for the Occurrence of Azeotropic Behavior

5.8 Solubility of Gases in Liquids

5.9 Liquid–Liquid Equilibria

5.10 Predictive Models

References

6 Caloric Properties

6.1 Caloric Equations of State

6.2 Enthalpy Description in Process Simulation Programs

6.3 Caloric Properties in Chemical Reactions

References

7 Electrolyte Solutions

7.1 Introduction

7.2 Thermodynamics of Electrolyte Solutions

7.3 Activity Coefficient Models for Electrolyte Solutions

7.4 Dissociation Equilibria

7.5 Influence of Salts on the Vapor–Liquid Equilibrium Behavior

7.6 Complex Electrolyte Systems

References

8 Solid–Liquid Equilibria

8.1 Introduction

8.2 Thermodynamic Relations for the Calculation of Solid–Liquid Equilibria

8.3 Salt Solubility

8.4 Solubility of Solids in Supercritical Fluids

Problems

References

9 Membrane Processes

9.1 Osmosis

9.2 Pervaporation

References

10 Polymer Thermodynamics

1

10.1 Introduction

10.2

g

Models

10.3 Equations of State

10.4 Influence of Polydispersity

10.5 Influence of Polymer Structure

References

11 Applications of Thermodynamics in Separation Technology

11.1 Introduction

11.2 Verification of Model Parameters Prior to Process Simulation

11.3 Investigation of Azeotropic Points in Multicomponent Systems

11.4 Residue Curves, Distillation Boundaries, and Distillation Regions

11.5 Selection of Entrainers for Azeotropic and Extractive Distillation

11.6 Selection of Solvents for Other Separation Processes

11.7 Selection of Solvent‐Based Separation Processes

References

12 Enthalpy of Reaction and Chemical Equilibria

12.1 Introduction

12.2 Enthalpy of Reaction

12.3 Chemical Equilibrium

12.4 Multiple Chemical Reaction Equilibria

References

13 Examples for Complex Systems

13.1 Introduction

13.2 Formaldehyde Solutions

13.3 Vapor Phase Association

References

14 Practical Applications

14.1 Introduction

14.2 Flash

14.3 Joule–Thomson Effect

14.4 Adiabatic Compression and Expansion

14.5 Pressure Relief

14.6 Limitations of Equilibrium Thermodynamics

References

15 Experimental Determination of Pure Component and Mixture Properties

15.1 Introduction

15.2 Pure Component Vapor Pressure and Boiling Temperature

15.3 Enthalpy of Vaporization

15.4 Critical Data

15.5 Vapor–Liquid Equilibria

15.6 Activity Coefficients at Infinite Dilution

15.7 Liquid–Liquid Equilibria (LLE)

15.8 Gas Solubility

15.9 Excess Enthalpy

References

16 Introduction to the Collection of Example Problems

16.1 Introduction

16.2 Mathcad Examples

16.3 Examples Using the Dortmund Data Bank (DDB) and the Integrated Software Package DDBSP

16.4 Examples Using Microsoft Excel and Microsoft Office VBA

Appendix A: Pure Component Parameters

Appendix B: Coefficients for High‐Precision Equations of State

References

Appendix C: Useful Derivations

A1 Relationship Between (∂

s

/∂

T

)

P

and (∂

s

/∂

T

)

v

A2 Expressions for (

∂

u

/∂

v)

T

and (

∂

s

/∂

v)

T

A3

c

P

and

c

v

as Derivatives of the Specific Entropy

A4 Relationship Between

c

P

and

c

v

A5 Expression for (∂h/∂P)

T

A6 Expression for (∂s/∂P)

T

A7 Expression for [∂(g/RT)/∂T]

P

and van't Hoff Equation

A8 General Expression for

c

v

A9 Expression for (∂P/∂v)

T

A10 Cardano's Formula

B1 Derivation of the Kelvin Equation

B2 Equivalence of Chemical Potential μ and Gibbs Energy g for a Pure Substance

B3 Phase Equilibrium Condition for a Pure Substance

B4 Relationship Between Partial Molar Property and State Variable (Euler Theorem)

B5 Chemical Potential in Mixtures

B6 Relationship Between Second Virial Coefficients of Leiden and Berlin Form

B7 Derivation of Expressions for the Speed of Sound for Ideal and Real Gases

B8 Activity of the Solvent in an Electrolyte Solution

B9 Temperature Dependence of the Azeotropic Composition

B10 Konovalov Equations

C1 (s–s)

T,P

C2 (h–h)

T,P

C3 (g–g)

T,P

C4 Relationship Between Excess Enthalpy and Activity Coefficient

D1 Fugacity Coefficient for a Pressure‐Explicit Equation of State

D2 Fugacity Coefficient of the Virial Equation (Leiden Form)

D3 Fugacity Coefficient of the Virial Equation (Berlin Form)

D4 Fugacity Coefficient of the Soave–Redlich–Kwong Equation of State

D5 Fugacity Coefficient of the PSRK Equation of State

D.6 Fugacity Coefficient of the VTPR Equation of State

E.1 Derivation of the Wilson Equation

E.2 Notation of the Wilson, NRTL, and UNIQUAC Equations in Process Simulation Programs

E.3 Inability of the Wilson Equation to Describe a Miscibility Gap

F.1 (h–h) for Soave–Redlich–Kwong Equation of State

F2 (s–s) for Soave–Redlich–Kwong Equation of State

F3 (g–g) for Soave–Redlich–Kwong Equation of State

F4 Antiderivatives of

Correlations

G1 Speed of Sound as Maximum Velocity in an Adiabatic Pipe with Constant Cross‐Flow Area

G2 Maximum Mass Flux of an Ideal Gas

References

Appendix D: Standard Thermodynamic Properties for Selected Electrolyte Compounds

Reference

Appendix E: Regression Technique for Pure Component Data

Appendix F: Regression Techniques for Binary Parameters

References

Appendix G: Ideal Gas Heat Capacity Polynomial Coefficients for Selected Compounds

Reference

Appendix H: UNIFAC Parameters

Further Reading

Appendxi I: Modified UNIFAC Parameters

Further Reading

Appendix J: PSRK Parameters

Further Reading

Appendix K: VTPR Parameters

References

Further Readings

Index

End User License Agreement

List of Tables

Chapter 2

Table 2.1 The specific state functions

u

,

h

,

s

,

g

, and

a

as a function of

T

,

P

, a...

Table 2.2 Residual properties for pressure‐ and volume‐explicit equations of sta...

Table 2.3 Typical accuracy demands for technical equations of state [29].

Table 2.4 Forms of the cubic equations of state.

Chapter 3

Table 3.1 Group contributions for the Joback method.

Table 3.2 Parameters for the Kechin equation.

Table 3.3 Change in vapor pressure of water droplets as a function of the drople...

Table 3.4 Impression on the quality of cubic equations of state for the predicti...

Table 3.5 Group contributions for estimating

with the Joback method.

Table 3.6 Dipole moment for a few substances [6] (1 Debye ≈ 3.336 · 10

−30

...

Table 3.7 Values for

Q

used in Eq. 3.146 .

Table 3.8 Structural groups for the evaluation of the diffusion volume using the...

Chapter 4

Table 4.1 Property changes of ideal mixtures.

Table 4.2 Residual parts of the particular thermodynamic quantities calculated w...

Table 4.3 Overview on important

g

E

mixing rules.

Chapter 5

Table 5.1 Number of experimental data required for a 10‐component system at a gi...

Table 5.2 Vapor–liquid equilibrium data for the system ethanol (1)–water (2) at ...

Table 5.3 Experimental data  [4] for the system ethanol (1)–water (2) at 70 °C...

Table 5.4 Excess enthalpy data  [16] for the system ethanol (1)–water (2) at...

Table 5.5 Wilson interaction parameters for the ternary system acetone (1)–chlor...

Table 5.6 Important expressions for the excess Gibbs energy and the derived acti...

Table 5.7 Types of VLE data published.

Table 5.8 Temperature‐dependent Wilson parameters for the system ethanol (1)–

n‐

...

Table 5.9 Recommended NRTL interaction parameters (cal/mol) for different binary...

Table 5.10 Recommended Wilson interaction parameters (cal/mol) for different bin...

Table 5.11 Recommended UNIQUAC interaction parameters (cal/mol) for different bi...

Table 5.12 Henry constants of various gases (1) in water (2) at 25 °C [5] .

Table 5.13 Henry constants (bar) of various gases in different organic liquids a...

Table 5.14 Experimental gas solubility data, fugacities, fugacity coefficients, ...

Table 5.15 Hypothetical liquid molar volumes and solubility parameters at

ϑ

 ...

Table 5.16 Molar volumes and solubility parameters for selected compounds.

Table 5.17 Experimental [5] and predicted solubilities of

n

‐hexane and cyclohex...

Table 5.18 Parameters for the empirical estimation of hydrocarbon solubilities i...

Table 5.19 Parameters for the empirical estimation of water solubilities in hydr...

Table 5.20 Main differences between the new group contribution equation of state...

Chapter 6

Table 6.1 Mass balance for the incremental flash in Example 6.2.

Chapter 7

Table 7.1 Heats of solution at infinite dilution in water for a few electrolytes...

Table 7.2 Relative dielectric constants of selected solvents at

T

 = 298.15 K.

Table 7.3 Coefficients for the calculation of the relative dielectric constant (...

Table 7.4 Selected interaction parameters for the LIQUAC model.

Table 7.5 UNIQUAC parameters (

K

) for selected solvents.

Table 7.6 Relative van der Waals volumes (

r

solv

) and van der Waals surface areas...

Chapter 8

Table 8.1 Thermodynamic standard properties for selected salts and ions in the a...

Chapter 10

Table 10.1 Iteration procedure for the calculation of a cloud point.

Table 10.2 Numerical results for the cloud‐point curve for the system H

2

O + MC15...

Table 10.3 Universal constants for the calculation of

a

I

in Eq. 10.45.

Table 10.4 Universal constants for the calculation of

b

I

in Eq. 10.45 .

Table 10.5 PC‐SAFT parameters for the system CO

2

(1) + PS 158 (2).

Table 10.6 Calculation of

a

i

and

b

i

values in Eq. 10.45 using Tables  10.3 and...

Chapter 11

Table 11.1 Current status of the Dortmund Data Bank (March 2018).

Table 11.2 Comparison of the predicted azeotropic data for the quaternary system...

Table 11.3 Comparison of the predicted azeotropic data for the quaternary system...

Table 11.4 Compositions in the liquid and vapor phase and pressure for the diffe...

Table 11.5 Selected entrainers for the separation of ethanol (1)–water (2) and w...

Table 11.6 Experimental and predicted separation factors at infinite dilution at...

Chapter 12

Table 12.1 Equilibrium conversion and composition of the NH

3

synthesis at differ...

Table 12.2 Calculated

i

‐butene conversions assuming ideal behavior, respectively,...

Table 12.3 Calculated mole numbers for the different steps of the relaxation met...

Table 12.4 Overview on the numbers of moles for the particular components.

Table 12.5 Iteration history in Example 12.9.

Chapter 13

Table 13.1 Main groups of the Maurer model with their volume and surface area pa...

Table 13.2 Group interaction parameters a

nm

(K) for the UNIFAC approach in the Ma...

Table 13.4 Antoine coefficients used in the Maurer model [6] : ln (

P

s

/kPa) = 

A

 ...

Table 13.5 Compressibility factors of associating substances at the normal boili...

Table 13.6 Association constants for the most important associating substances.

Table 13.7 VLE data for the system water (1)–acetic acid (2) at 80 °C [34,35]....

Chapter 14

Table 14.2 Iterative solution for the pressure in the vessel at

T

2

 = 400 K.

Table 14.3 Iteration history for Example 14.5.

Table 14.4 Iteration history for Example 14.6.

6

Table F.1 LLE data of the system 1,1,2‐trichloroethane (1)–water (2).

List of Illustrations

Chapter 2

Figure 2.1

PvT

diagram.

Figure 2.2

Pv

diagram.

Figure 2.3 Isochoric changes of state in the

Pv

diagram.

Figure 2.4 Critical opalescence of ethane. (a)

T

 = 

T

c

 − 0.5 K; (b)

T

 = 

T

c

 = 305...

Figure 2.5

PT

diagram.

Figure 2.6 Two arrangements for the heating of a gas.

Figure 2.7 Illustration of the residual part of the Gibbs energy using the isot...

Figure 2.8 Temperature change of water between

ϑ

1

 = 50 °C and

ϑ

2

 = 15...

Figure 2.9

PvT

data of water for the determination of the second virial coeffic...

Figure 2.10 Temperature dependence of the second virial coefficient of nitrogen...

Figure 2.11 Specific heat capacity

c

P

of ethylene at

P

 = 70 bar as a function o...

Figure 2.12 Zeno line, Joule–Thomson inversion curve, and Boyle curve for nitro...

Figure 2.13 Mathematical representation of the calculated

PvT

behavior with the...

Figure 2.14 Isotherm for ethanol at

ϑ

 = 200 °C in the

Pv

diagram, calculat...

Figure 2.15 Maxwell's equal area construction to determine the vapor pressure, ...

Figure 2.16 Definition of the acentric factor, exemplified for ethanol. Experim...

Figure 2.17 Relative deviations between experimental and calculated liquid mola...

Figure 2.18 Calculation route for the enthalpy of vaporization.

Figure 2.19 Representation of the liquid heat capacities of toluene, methanol, ...

Figure 2.20 Representation of the liquid heat capacities of

n

‐pentane (a) and e...

Chapter 3

Figure 3.1 Structural formula of

m

‐xylene.

Figure 3.2 Structural formula of pentylcyclohexane.

Figure 3.3 Structural formula of methylcyclohexane.

Figure 3.4 Description of the pressure dependence of the melting point using th...

Figure 3.5 Qualitatively wrong representation of

of nitrogen at low temperatu...

Figure 3.6 Diagram types for the vapor pressure as a function of temperature (e...

Figure 3.7 Structural formula of

n

‐propyl benzene.

Figure 3.8 Typical shape of a saturated liquid density plot (substance: propyle...

Figure 3.9 Density deviation plot for R125 (pentafluoroethane) for the PPDS and...

Figure 3.10 Mixture density for the system

n

‐hexane–chloroform at

ϑ

 = 50 ...

Figure 3.11 Deviation plots for the enthalpy of vaporization of propane using t...

Figure 3.12 Enthalpies of vaporization as a function of temperature for some se...

Figure 3.13 Specific isobaric heat capacities of ideal gases as functions of te...

Figure 3.14 Liquid specific heat capacity of water as a function of temperature...

Figure 3.15 Difference between

and

c

σ

for R134a (1,1,1,2‐tetrafluoroetha...

Figure 3.16 Comparison between polynomial and PPDS equation for the correlation...

Figure 3.17 Explanation of the viscosity of a Newtonian fluid.

Figure 3.18 Dynamic viscosity of saturated liquid water as a function of temper...

Figure 3.19 Deviation plots of the PPDS and the extended Kirchhoff equation for...

Figure 3.20 Dynamic viscosity of liquid R134a (1,1,1,2‐tetrafluoroethane) as a ...

Figure 3.21 Liquid viscosity of the system methanol (1)–water (2) at different ...

Figure 3.22 Dynamic viscosity of gaseous water as a function of temperature.

Figure 3.23 Dynamic viscosity of gaseous

n

‐pentane as a function of pressure.

Figure 3.24 Dynamic viscosity as a function of concentration for the system nit...

Figure 3.25 Thermal conductivity of water and toluene as a function of temperat...

Figure 3.26 Pressure dependence of the liquid thermal conductivity of toluene a...

Figure 3.27 Liquid thermal conductivity as a function of concentration for the ...

Figure 3.28 Thermal conductivity of gaseous water as a function of temperature.

Figure 3.29 Experimental data and Stiel–Thodos estimation for the thermal condu...

Figure 3.30 Vapor thermal conductivity as a function of concentration for the s...

Figure 3.31 Forces on molecules in the bulk and in the surface layer.

Figure 3.32 Surface tension of water as a function of temperature.

Figure 3.33 Surface tension of a liquid mixture of octanoic acid ethyl ester (1...

Chapter 4

Figure 4.1 The property change of mixing for a binary system.

Figure 4.2 The partial molar properties for a binary mixture.

Figure 4.3 The Gibbs energy change of mixing, the ideal Gibbs energy change of ...

Figure 4.4 Vapor–liquid equilibrium of the system 2‐propanol (1) + water (2). (...

Figure 4.5 Histograms to justify the assumption of a constant

u

‐value.

Figure 4.6 Calculation of the excess Gibbs energies for a symmetric (a) and an ...

Figure 4.7 Dependence of the ratios

b

i

/

b

ethane

and

r

i

/

r

ethane

on the chain leng...

Figure 4.8 Representation of vapor–liquid equilibria of the system ethane (1)–

n

Chapter 5

Figure 5.1 Simplified structure of a conventional chemical plant.

Figure 5.2 Equilibrium stage and typical separation problem.

Figure 5.3 Seven liquid phases in equilibrium with the vapor phase.

Figure 5.4

Pxy

diagram for the system ethanol (1)–water (2) at 70 °C [4].

Figure 5.5 Illustration of the law of opposite lever arms on the basis of the b...

Figure 5.6

Pxy

diagram for the system nitrogen (1)–methane (2) at different tem...

Figure 5.7 Experimental vapor pressures of ethane and heptane and experimental ...

Figure 5.8 (a–c) The three different types of critical VLE behavior for the cas...

Figure 5.9 VLE behavior of the following binary systems near the critical point...

Figure 5.10

K

‐Factors for the binary system nitrogen (1)–methane (2) as a funct...

Figure 5.11 Isoplethic

PT

diagram of a natural gas mixture with seven compounds...

Figure 5.12 Ternary phase equilibrium diagram for the system ethanol–water–benz...

Figure 5.13 φ

i

values for the system ethanol (1)–water (2) at 70 °C.

Figure 5.14 Concentration dependence of the activity coefficients and of the di...

Figure 5.15 Different types of vapor–liquid equilibrium diagrams for the follow...

Figure 5.16 Contribution of the different parameters of the Redlich–Kister expa...

Figure 5.17 Excess Gibbs energy, excess enthalpy, and −

Ts

E

for the system ethan...

Figure 5.18 Selected excess enthalpy data at different temperatures for the sys...

Figure 5.19 Excess volumes of the system ethanol (1)–water (2) at 20 °C [5] .

Figure 5.20 Excess volume of the system ethanol (1)–water (2) at 323 K as a fun...

Figure 5.21 Representation of the temperature dependence of the activity coeffi...

Figure 5.22 Calculated activity coefficients of the monomer and resulting syste...

Figure 5.23 Experimental [ 5 , 24 ] and calculated vapor phase mole fractions...

Figure 5.24 Experimental

Tx

data [ 5 , 24 ] and calculated

Tx

behavior of the...

Figure 5.25 Flow diagram for the calculation of isobaric VLE data assuming idea...

Figure 5.26 Flow diagram for the calculation of isothermal VLE taking into acco...

Figure 5.27 Check of isothermal complete VLE data of the system ethanol (1)–wat...

Figure 5.28 Flow diagram of the consistency test.

Figure 5.29 Results for the binary system 2‐propanol (1)–

tert

‐butanol (2) at 40...

Figure 5.30 Example page of the VLE Data Collection [12] .

Figure 5.31 Result of the fit of temperature‐independent Wilson parameters to c...

Figure 5.32 Calculated results for the VLE at 1 atm, activity coefficients

γ

...

Figure 5.33 Influence of the error of the separation factor on the minimum numb...

Figure 5.34 Results for acetone (1)–water (2) using recommended temperature‐dep...

Figure 5.35 Results for acetone (1)–water (2) using the NRTL parameters provide...

Figure 5.36 Experimental [5] and calculated vapor pressures for selected sol...

Figure 5.37 Experimental [5] and calculated enthalpies of vaporization using...

Figure 5.38 Experimental and calculated liquid densities using the PR equation ...

Figure 5.39 Experimental and calculated liquid densities using the volume‐trans...

Figure 5.40 Experimental [5] and calculated liquid heat capacities using VTP...

Figure 5.41 VLE results with the Soave–Redlich–Kwong equation of state for the ...

Figure 5.42 Experimental and calculated VLE data for the system acetone (1)–wat...

Figure 5.43 Experimental and calculated VLE data for the system isopropanol (1)...

Figure 5.44 Experimental and correlated VLE,

h

E

, azeotropic, and

γ

∞

...

Figure 5.45 Flow diagram for the calculation of isothermal vapor–liquid equilib...

Figure 5.46 Experimental [5] and predicted

K

‐factors for the system N

2

–CO

2

–H

Figure 5.47 Examination of the azeotropic behavior of binary homogeneous system...

Figure 5.48 Temperature dependence of ln 

(‐ ‐) calculated with the help of th...

Figure 5.49 Azeotropic behavior of the system ethanol (1)–1,4‐dioxane (2) (a) a...

Figure 5.50 Ratio of the activity coefficients

γ

1

/

γ

2

and ratio of the...

Figure 5.51

(—) and the ratio of the vapor pressures

in logarithmic form ...

Figure 5.52 Experimental and predicted azeotropic composition of the system ace...

Figure 5.53 Experimental and predicted excess enthalpies of the system acetone ...

Figure 5.54 Experimental and predicted azeotropic composition of the system eth...

Figure 5.55 Vapor pressure of ethanol and benzene as a function of the inverse ...

Figure 5.56 Experimental azeotropic points of water (1)–deuterated water (2) [ ...

Figure 5.57 Predicted contour lines (

α

ij

 = 1) using modified UNIFAC for th...

Figure 5.58 Experimental and calculated LLE behavior using modified UNIFAC for ...

Figure 5.59 Experimental solubilities [5] of CO

2

in methanol (▴ ) and aqueou...

Figure 5.60 Chemical reactions that have to be considered besides the gas solub...

Figure 5.61 Henry constants of He, N

2

, and O

2

in water as a function of tempera...

Figure 5.62 Henry constants of various gases in organic solvents as a function ...

Figure 5.63

f

1

/

x

1

(

p

1

/

x

1

) (resp.

f

1

) as a function of

x

1

for the system CO

2

(1)–...

Figure 5.64 Henry constant of CO

2

in the system methanol (1)–water (2) at 25 °C...

Figure 5.65 Experimental and calculated

Px

data using the SRK equation of state...

Figure 5.66 Temperature dependence of the reduced standard fugacity of the solu...

Figure 5.67 Observed temperature dependences of binary LLE [5] . (a) 1‐butano...

Figure 5.68 The most important types of ternary LLE [5] at a temperature of ...

Figure 5.69 Experimental [5] and calculated distribution coefficients of eth...

Figure 5.70 Concentration dependence of the molar Gibbs energy for systems with...

Figure 5.71 Graphical determination of LLE for binary systems exemplary shown f...

Figure 5.72 Experimental and calculated VLE and azeotropic data using the UNIQU...

Figure 5.73 Flow diagram for the calculation of LLE using the

K

‐factor method.

Figure 5.74 The first three steps of the

K

‐factor method together with the expe...

Figure 5.75 Qualitative progress of the temperature dependence of ternary liqui...

Figure 5.76 LLE behavior of the ternary system tetrahydrofuran–water–phenol as ...

Figure 5.77 Excess volumes and LLE behavior of the system tetrahydrofuran (1)–w...

Figure 5.78 Excess volumes and LLE behavior of the system methanol (1)–

n

‐heptan...

Figure 5.79 Group contribution concept.

Figure 5.80 Experimental and predicted

y

–

x

data for the system

n

‐hexane (1)–2‐b...

Figure 5.81 Experimental [5] and predicted VLE data for alkane–ketone system...

Figure 5.82 Experimental [5] and predicted excess enthalpies using UNIFAC of...

Figure 5.83 Status (2017) of the modified UNIFAC method.

Figure 5.84 Available excess enthalpy data as a function of temperature.

Figure 5.85 Mean absolute deviation in vapor‐phase mole fraction, temperature, ...

Figure 5.86 Experimental [5] and predicted excess enthalpies for different b...

Figure 5.87 Experimental and predicted results for the system acetone (1)–hexan...

Figure 5.88 Experimental and predicted results for different phase equilibria f...

Figure 5.89 Experimental [5] and predicted activity coefficients at infinite...

Figure 5.90 Experimental [5] and predicted solubilities

c

(mol/l) of alkanes...

Figure 5.91 Experimental and predicted VLE data using PSRK for the systems etha...

Figure 5.92 Status (2017) of the parameter matrix of the group contribution equ...

Figure 5.93 Experimental and predicted VLE data using PSRK for various CO

2

–alka...

Figure 5.94 Experimental and predicted VLE and azeotropic and critical data of ...

Figure 5.95 Experimental [9] and predicted

K

‐factors for a 12‐component system ...

Figure 5.96 Experimental and predicted (PSRK + LIFAC) results for the system CO

Figure 5.97 Experimental and predicted VLE data for symmetric alkane–alkane sys...

Figure 5.98 Experimental and predicted VLE data for asymmetric alkane–alkane sy...

Figure 5.99 Experimental and predicted VLE data for different CO

2

–alkane system...

Figure 5.100 Experimental and predicted VLE data, azeotropic points, and critic...

Figure 5.101Figure 5.101 Experimental and predicted excess enthalpy data for th...

Figure 5.102 Experimental and predicted SLE data for the system ethane (1)–CO

2

...

Figure 5.103 Experimental and predicted phase equilibrium data and excess entha...

Figure 5.104 Experimental and predicted LLE data using VTPR for the ternary sys...

Figure 5.105 Experimental [9] and predicted

K

‐factors for a 12‐component sys...

Figure 5.106 Experimental and calculated liquid densities using PSRK and VTPR f...

Figure 5.107 Experimental and predicted densities for the binary system acetone...

Figure 5.108 Correlation results of the equation of state VTPR for the system a...

Figure P5.6P5.6 Home glass distillery.

Chapter 6

Figure 6.1 Calculation of the liquid enthalpy of 1,1,1,2‐tetrafluoroethane (R1...

Figure 6.2 Results for

of water as a function of temperature using Route A.

Figure 6.3 Two fits of the enthalpy of vaporization of water.

Figure 6.4 Slopes of the two fits in Figure  6.3 .

Figure 6.5 Improved calculation for

of acetic acid.

Figure 6.6 Acceptable representation of the enthalpy of vaporization of acetic ...

Figure 6.7 Calculation of the enthalpy of saturated vapor using Route B.

Figure 6.8 Inlet and outlet streams of the combustor.

Chapter 7

Figure 7.1 Schematic structure of an aqueous electrolyte solution.

Figure 7.2 Illustration of the standard state of an electrolyte solution.

Figure 7.3 Experimental mean ionic activity coefficients for different salts in...

Figure 7.4 Mean logarithmic ionic activity coefficient for different aqueous sy...

Figure 7.5 Three types of cells according to the assumptions of like‐ion repuls...

Figure 7.6 Experimental and predicted mean ion activity coefficients of Na

2

SO

4

...

Figure 7.7 Osmotic coefficient of water as a function of the Na

2

SO

4

concentrati...

Figure 7.8 Influence of salts on the vapor–liquid equilibrium behavior.

Figure 7.9 Vapor–liquid equilibrium diagram for the ternary system methyl aceta...

Figure 7.10 Phase and reaction equilibria in the system CO

2

–NH

3

–H

2

O.

Chapter 8

Figure 8.1 Selected types of SLE. (a) Benzene (1)–naphthalene (2); (b) anthrac...

Figure 8.2 Vapor pressures and sublimation pressures of naphthalene – hypotheti...

Figure 8.3 Thermodynamic cycle for the derivation of an expression for the rati...

Figure 8.4 Experimental [4] and calculated SLE of benzene (2) with the differen...

Figure 8.5 Experimental and calculated SLE behaviors of the system ethanol (1)–...

Figure 8.6 Predicted SLE diagram and eutectic lines for the ternary system

o

‐xy...

Figure 8.7 Experimental and predicted SLE data for the system carbon tetrachlor...

Figure 8.8 Experimental and predicted solubilities of naphthalene (3) in ethano...

Figure 8.9 Experimental and calculated SLE behaviors for the system anthracene ...

Figure 8.10 Experimental and calculated SLE behaviors using the Porter model (

B

Figure 8.11 Experimental (•) and calculated SLE behavior of the systems

p

‐xylen...

Figure 8.12 Solid–liquid equilibria of the system lauric acid (1)–myristic acid...

Figure 8.13 Experimental, ideal, and predicted salt solubilities using LIQUAC a...

Figure 8.14 Mean activity coefficients of (a) NaCl, (b) KCl, and (c) NH

4

Cl in w...

Figure 8.15 Experimental and predicted solubilities of sodium sulfate (a) and m...

Figure 8.16 Starting point for the derivation of the required equations for the...

Figure 8.17 Experimental and predicted solubility (salt‐free basis) of KCl in t...

Figure 8.18 Experimental and calculated solubilities for the systems CO

2

(1)–oc...

Chapter 9

Figure 9.1 Osmosis, osmotic equilibrium, and reverse osmosis.

Figure 9.2 Principle of a membrane separation process.

Chapter 10

Figure 10.1 Differential (a) and integral (b) Schulz–Flory distribution functi...

Figure 10.2 Liquid–liquid equilibrium of binary polymer solutions at constant p...

Figure 10.3 Schematic picture of the Flory–Huggins lattice.

Figure 10.4 Schematic drawing of the Gibbs energy of the quasi‐binary polymer s...

Figure 10.5 Comparison of experimental (M. Haberer and B.A. Wolf, private commu...

Figure 10.6 Comparison of experimental [4] and calculated phase diagram for the...

Figure 10.7 Parameter estimation for the example H

2

O + MC150 without point 9 in...

Figure 10.8 Comparison of experimental [5] and calculated phase behavior of the...

Figure 10.9 Isothermal phase behavior of the system PS + MCH at different tempe...

Figure 10.10 Schematic drawing of the potential

u

(

r

) given in Eq. 10.31 .

Figure 10.11 Experimental [31] and calculated [22] demixing pressure of poly...

Figure 10.12 Comparison between experimental data ((a) density of the mixture ...

Figure 10.13 Comparison between experimental and calculated cloud‐point pressur...

Figure 10.14 Schematic liquid–liquid phase diagram for a polydisperse polymer i...

Figure 10.15 Fractionation effect.

Figure 10.16 Cloud‐point pressures in the system LLDPE + ethylene at different ...

Figure 10.17 Comparison between experimental [46] and calculated [47] demixi...

Chapter 11

Figure 11.1 Rough structure of the program package DDBSP.

Figure 11.2 Fields of application of thermodynamic models (

g

E

models, EOS, and ...

Figure 11.3 Experimental [7] and calculated dynamic viscosities for hexafluorob...

Figure 11.4 Verification of Wilson parameters, with the help of experimental da...

Figure 11.5 Separation factors obtained for the system acetone (1)–water (2) at...

Figure 11.6 Separation factors of the system acetone (1)–water (2) at 101.325 k...

Figure 11.7 Separation factors obtained for the system acetone (1)–water (2) at...

Figure 11.8 Calculated separation factors

α

12

at atmospheric pressure for ...

Figure 11.9 Calculated separation factors

α

12

at atmospheric pressure for ...

Figure 11.10 Experimental [7] and calculated separation factors at atmospher...

Figure 11.11 Composition as a function of time for two ternary systems in the c...

Figure 11.12 Boiling temperatures of the singular points for different ternary ...

Figure 11.13 Residue curves and distillation boundaries for different ternary s...

Figure 11.14 Phase equilibrium behavior of the ternary system acetone–chlorofor...

Figure 11.15 Calculated residue and distillation boundary for the system carbon...

Figure 11.16 Separation of azeotropic systems by azeotropic (feed F: pyridine–w...

Figure 11.17 Flow diagrams for the selection of suitable solvents for azeotropi...

Figure 11.18 Calculated separation factors and

y

–

x

behavior of the system benze...

Figure 11.19 Experimental [7] and predicted Henry constants using PSRK for t...

Figure 11.20 Column configuration for the separation of aliphatics from aromati...

Figure 11.21 Ratio of the vapor pressures and ratio of the predicted and experi...

Figure 11.22 Ratio of the vapor pressures

, predicted ratio of the activity co...

Chapter 12

Figure 12.1 Thermodynamic cycle for the calculation of the enthalpy of reaction...

Figure 12.2 Enthalpy of reaction of the ammonia synthesis at 450 °C as a functi...

Figure 12.3 Typical curve of the Gibbs energy for a reacting mixture.

Figure 12.4 Qualitative trend of the equilibrium conversion

X

for reversible ex...

Figure 12.5 Equilibrium conversion (

X

max

) and conversion for a limited residenc...

Figure 12.6 Experimental and calculated equilibrium conversions as a function o...

Figure 12.7 Experimental and calculated equilibrium constant

K

P

as a function o...

Figure 12.8 Experimental and predicted equilibrium conversion for the MTBE synt...

Figure 12.9 Experimental and predicted equilibrium conversion of

i

‐butene for t...

Figure 12.10 Schematic presentation of the relaxation method for the determinat...

Figure 12.11 Composition dependence of the molar Gibbs energy at 298.15 and 400...

Figure 12.12 Mole fractions of CH

4

, H

2

O, CO, H

2

, and CO

2

in chemical equilibriu...

Figure 12.13 Plot and detail magnification of the specific Gibbs energy in Exam...

Chapter 13

Figure 13.1 The system formaldehyde (1)–water (2) at

T

 = 423 K..

Figure 13.2 The system formaldehyde (1)–methanol (2) at

T

 = 333.1 K..

Figure 13.3 Specific heat capacity of gaseous HF as a function of temperature..

Figure 13.4

of acetic acid vapor as a function of temperature.

Figure 13.5 Enthalpy of vaporization as a function of temperature for HF and ac...

Figure 13.6 Phase diagram for the water (1)–acetic acid (2) system.

Figure 13.7 Phase diagram for the R22 (1)–HF (2) system..

Figure 13.8 Activity coefficients calculated for the system water (1)–acetic ac...

Chapter 14

Figure 14.1 Illustration of the flow in an orifice of a pipe.

Figure 14.2 Scheme of a refrigeration unit.

Figure 14.3 Steps for the pressure relief calculation.

Figure 14.4 Flow through actuated rupture disk.

Figure 14.5 Mass flux for a given temperature and pressure as a function of the...

Figure 14.6 Illustration of the two‐film theory.

Chapter 15

Figure 15.1 Cottrell's ebulliometer as modified by Washburn employing the Cott...

Figure 15.2 Isoteniscope for the static measurement of the vapor pressure of pu...

Figure 15.3 Apparatus for measurement of low vapor pressures by the Knudsen eff...

Figure 15.4 Experimental setup for saturated liquid–vapor pressure via transpir...

Figure 15.5 Development of the number of different VLE data types with publicat...

Figure 15.6 Swietoslawski ebulliometer modified by Rogalski and Malanowski [26...

Figure 15.7 Computer‐operated static VLE apparatus by Rarey and Gmehling [28] ...

Figure 15.8 Typical result of a static VLE measurement for the mixture ethyl

te

...

Figure 15.9 Apparatus for degassing pure substances..

Figure 15.10 Thermostatted headspace cell.

Figure 15.11 Static high‐pressure VLE apparatus with ROLSI [39]. Courtesy of D....

Figure 15.12 ROLSI [40] . Courtesy of D. Richon.

Figure 15.13 Internal representation of electromagnetic ROLSI IV [42]. Courtesy...

Figure 15.14 Inert gas stripping apparatus for the determination of

γ

∞

...

Figure 15.15 Simple thermostatted flask with sampling ports for the analytic de...

Figure 15.16 Isothermal flow calorimeter (Hart Scientific 7501) [39] .

Chapter 16

Figure 16.1 Excerpt from a typical Mathcad document from the example collectio...

Figure 16.2 Experimental VLE data set and curve calculated using UNIFAC as pres...

Guide

Cover

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E1

Chemical Thermodynamics for Process Simulation

Jürgen Gmehling, Michael Kleiber, Bärbel Kolbe, and Jürgen Rarey

Second, Completely Revised and Enlarged Edition

Copyright

Authors

Prof. Dr. Jürgen Gmehling

Carl von Ossietzky Univ. Oldenburg

Fakultät V ‐ Mathematik und Naturwissenschaften

Institut für Chemie ‐ Technische Chemie

26111 Oldenburg

Germany

Dr.‐Ing. Michael Kleiber

thyssenkrupp Industrial Solutions AG

Friedrich‐Uhde‐Str. 2

65812 Bad Soden

Germany

Dr.‐Ing. Bärbel Kolbe

thyssenkrupp Industrial Solutions AG

‐ now retired ‐

Germany

Dr. Jürgen Rarey

Carl von Ossietzky Univ. Oldenburg

Fakultät V ‐ Mathematik und Naturwissenschaften

Institut für Chemie ‐ Technische Chemie

26111 Oldenburg

Germany

Cover  The cover image was kindly provided by Mark Gmehling

All books published by Wiley‐VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.

Library of Congress Card No.:

applied for

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the Deutsche Nationalbibliothek

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© 2019 Wiley‐VCH Verlag GmbH & Co. KGaA, Boschstr. 12, 69469 Weinheim, Germany

All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form – by photoprinting, microfilm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law.

Print ISBN: 978‐3‐527‐34325‐6

ePDF ISBN: 978‐3‐527‐80945‐5

ePub ISBN: 978‐3‐527‐80944‐8

oBook ISBN: 978‐3‐527‐80947‐9

Cover Design SCHULZ Grafik‐Design, Fußgönheim, Germany

Preface

More than 20 years ago, the first edition of the textbook Thermodynamics was published in German language.

Its target was to demonstrate the basic principles, how thermodynamics can contribute to solve manifold kinds of problems in gas, oil, and chemical processing, in pharmaceutical and food production, in environmental industry, in plant design by engineering companies, and also for institutions dealing with hazardous materials like the fire brigade, transport companies, or the technical supervisory associations. For all these purposes, it is often decisive to have a profound knowledge of the thermophysical properties, transport properties, phase equilibria, and chemical equilibria. Therefore, a large part of the first edition and also of this completely new edition is dedicated to the evaluation of these quantities. The mentioned properties are also helpful in the evaluation of nonequilibrium properties such as kinetic data and reaction rates, which are not subject of this book.

Databases filing published experimental physical properties and phase equilibrium data are a prerequisite for developing thermodynamic models and for determining reliable model parameters, which describe the problem to be solved with adequate accuracy. A long way has been covered since the beginning of the professional filing of phase equilibrium data. Starting with a few hundred compounds in 1973, pure component and mixture properties for more than 74 000 components can now be found in the Dortmund Data Bank (DDB). A great step forward in modeling was the further development of the solution of group concept, which makes the prediction of, for example, phase equilibria possible. A lot of experimental work was performed to systematically fill the gaps where no data for the determination of group interaction parameters were available. Together with the fast‐developing computer technology and on the basis of professional databases like the DDB, process simulators nowadays allow rapid calculation of phase equilibria, transport properties, caloric data, various thermophysical properties, and chemical equilibria. Even the thermodynamics of large industrial processes is routinely modeled using commercial process simulators. While a large variety of models and model options can be selected by a simple mouse click, the task of the engineer or chemist remains to choose the most appropriate model, and one should be aware of its accuracy, its possible limitations, and the quality of the model parameters for the system of interest. A thorough understanding of thermodynamics is still obligatory; otherwise misconceptions of processes or design errors are the consequences.

The new edition of the textbook, now written in the English language, is called Chemical Thermodynamics for Process Simulation. It specifically targets readers working in the fields of process development, process synthesis, or process optimization and therefore presents the fundamentals of thermodynamics not only for students but also on the level required for experienced process engineers. The most important models that are applied in process industry are thoroughly explained, as well as their adjustment with the help of factual databases (data regression). Cubic equations of state with gE mixing rules present a great step forward toward a universal model for both subcritical and supercritical systems and are therefore emphasized.

In addition, models for special substances like carboxylic acids, hydrogen fluoride, formaldehyde, electrolytes, and polymers are introduced, and the capabilities of high‐precision equations of state and various predictive methods are explained. Recommendations for the parameter fitting procedure and numerous hints to avoid pitfalls during process simulation are given. Because of the space limitation in the book, we were not able to cover the whole range of thermodynamics, for example, adsorption has been left out completely as it cannot be presented within a short chapter.

The English language was chosen to extend the readership to students and engineers from all over the world. Although none of the authors is a native speaker, we found it even more convenient to describe the particular issues in the language generally used in scientific publications.

The team of four authors with considerably different backgrounds reflects the importance of thermodynamics in both academia and industrial applications. The authors present their biography and special research interests on separate pages following this preface.

In contrast to other textbooks on thermodynamics, we assume that the readers are familiar with the fundamentals of classical thermodynamics, which are the definitions of quantities like pressure, temperature, internal energy, enthalpy, entropy, and the three laws of thermodynamics, which are very well explained in other textbooks. We therefore restricted ourselves to only a brief introduction and devoted more space to the description of the real behavior of the pure compounds and their mixtures. The ideal gas law is mainly used as a reference state; for application examples, the real behavior of gases and liquids is calculated with modern gE models, equations of state, and group contribution methods.

Of course, by taking into account the real behavior, the solution of the examples becomes much more complex, but at the same time they are closer to industrial practice. For a textbook, there is a difficulty to describe the typical iterative procedures in phase equilibrium and process calculations. In order to achieve a better understanding, we decided to provide Mathcad sheets and DDBST programs so that the reader has the chance to reproduce the examples on his own. Mathcad was chosen because of its convenient way to write equations in close‐to‐textbook form and without cryptic variable names. We prefer SI units but do not stick to them obsessively. In the examples and diagrams, we used the most convenient units. We think that the parallel use of various units will remain the status quo for the time being, and engineers and chemists should be able to cope with this situation. We are aware that the current value of the gas constant is R = 8.31447 J/(mol K). However, still many applications are based on the old value R = 8.31433 J/(mol K). Luckily, except for the high‐precision equations of state, this distinction is by far beyond the accuracy scope of our calculations.

For a complete understanding, mathematical derivations can often not be avoided or are even necessary for the understanding. If they interrupt the flow of the presentation, we have moved them to a special chapter in the appendix, so that the reader can follow the main ideas more easily. Of course, no textbook can cover all possible and interesting derivations, but we hope that the reader will gain a feeling for the methodology in thermodynamics and is able to carry out similar derivations on his own.

We hope that this book closes a gap between scientific development and its application in industry. We are grateful to all the people who gave us valuable support and advice during the compilation of the manuscript. None of the authors were capable to write an adequate chapter on polymer thermodynamics. Therefore we are especially obliged to Prof. Dr. Sabine Enders. She wrote an excellent chapter fully in line with the targets and structure of this book. Many other people gave valuable advice. We are thankful to Prof. Dr. Wolfgang Wagner, Prof. Dr. Hans Hasse, Prof. Dr. Josef Novak, Prof. Dr. Roland Span, Todd Willman, Dr. Michael Sakuth, Ingo Schillgalies, Jens Otten, Dr. André Mohs, Dr. Bastian Schmid, Dr. Jens Ahlers, Dr. Silke Nebig, Dr. Torben Laursen, Dr. Heiner Landeck, Prof. Dr. Ravi Prasad Andra, Dr. Michael Benje, Dr. Kari Keskinen, the colleagues from DDBST GmbH, and the research group at the Carl von Ossietzky University of Oldenburg, who provided many impressive figures of the book. Furthermore, we are deeply thankful to our families for supporting us during all the time.

Jürgen Gmehling

Michael Kleiber

Bärbel Kolbe

Jürgen Rarey

Preface to the Second Edition

Seven years have passed since the first edition of our textbook Chemical Thermodynamics for Process Simulation had been published. We intended to write a book with the special focus on the thermodynamics that can be directly used in process simulation. We are proud that we got excellent feedback from many people, and after such a long time, we think we are ready for the second edition.

The main supplement is a chapter on experimental methods. The situation where the data available are not sufficient will frequently occur in process simulation, and one has to decide whether and which additional data are necessary. It is useful to know what the particular opportunities are. Due to the manifold options, our chapter cannot be a comprehensive survey of all methods. Instead, we think that it is a good approach to give an overview on the most important methods, especially for phase equilibrium measurements. With this chapter, we want to cover the whole chain of physical property management in process simulation, ranging from measurement, inquiry, correlation, and application.

Furthermore, we considered a lot of suggestions from our readers. Especially, the authors are grateful to Prof. Dr. Hans Huemer, Prof. Dr. Ulrich Deiters, Prof. Dr. Harald Klein, and Dr. Silke Ahlers for their valuable help during the preparation of the second edition of our textbook. We are, like any author, annoyed with ourselves about any misprint we have been confronted with but, on the other hand, grateful as this is the only chance to overcome them. We hope that we have made some progress in this area, as any misprint disturbs the reading flow of the book if such an exact science as thermodynamics is regarded.

Jürgen Gmehling

Bärbel Kolbe

Michael Kleiber

Jürgen Rarey

List of Symbols

a

attractive parameter in cubic equations of state

(J m

3

)/mol

2

a

specific Helmholtz energy

J/mol, J/kg

a

i

activity of component

i

a

ij

,

b

ij

,

c

ij

, d

ij

binary or group interaction parameter in local composition models (Wilson, NRTL, UNIQUAC, UNIFAC, …)

A

Helmholtz energy

J

A

area

m

2

A

m

parameter in Debye–Hückel equation

kg

0.5

mol

0.5

a, b, c, …

constants in pure component property correlations

A, B, C, …

constants in pure component property correlations

A

n

,

B

n

parameters for the description of association reactions of degree

n

A

ϕ

parameter in Pitzer–Debye–Hückel term

b

repulsive parameter in equations of state

m

3

/mol

B

second virial coefficient

m

3

/mol

B

ij

parameter in Pitzer equation

B

ij

cross second virial coefficient

m

3

/mol

c

volume concentration

mol/m

3

c

P

specific isobaric heat capacity

J/(mol K), J/(kg K)

c

v

specific isochoric heat capacity

J/(mol K), J/(kg K)

c

σ

specific liquid heat capacity along the saturation line

J/(mol K), J/(kg K)

C

third virial coefficient

(m

3

)

2

/mol

2

d

droplet diameter

m

d

i

segment diameter (PC‐SAFT)

m

D

ij

diffusion coefficient of component

i

in component

j

m

2

/s

e

elementary charge;

e

 = 1.602189 · 10

−19

C

E

Ackermann correction factor

f

i

fugacity of component

i

Pa

F

objective function

F

Faraday's constant;

F

 = 96 484.56 C/mol

F

i

surface area/mole fraction of component

i

(UNIQUAC, UNIFAC)

—

F

(r)

integral distribution function

F

ij

force between two ions

i

and

j

N

g

specific Gibbs energy

J/mol

Δ

g

Gibbs energy of mixing

J/mol

Δ

g

ij

interaction parameter of the NRTL equation

K

standard Gibbs energy of reaction

J/mol

G

Gibbs energy

J

h

Planck's constant;

h

 = 6.626069 · 10

−34

 Js

h

specific enthalpy

J/mol, J/kg

standard enthalpy of formation

J/mol

standard Gibbs energy of formation

J/mol

standard enthalpy of reaction

J/mol

Δ

h

m

specific enthalpy of fusion

J/mol, J/kg

h–h

id

specific isothermal enthalpy difference between the actual and ideal gas state, calculated with an EOS

J/mol

specific enthalpy of solution of Henry component

i

J/mol

Δ

h

sol

enthalpy of solution

J/mol, J/kg

Δ

h

v

specific enthalpy of vaporization

J/mol, J/kg

H

enthalpy

J

H

ij

Henry constant of component

i

in solvent

j

Pa

I

ionic strength

mol/kg

I

x

molar ionic strength

mol/mol

J

i

flux through membrane of component

i

kg/(s m

2

)

k

Boltzmann's constant;

k

 = 1.38048 · 10

−23

 J/K

k

ij

binary interaction parameter in cubic equations of state

K

chemical equilibrium constant

K

liquid–liquid distribution coefficient

K

cry

cryoscopic constant

K kg/mol

K

sp

solubility product

K

n

chemical equilibrium constant for association of degree

n

K

in

chemical equilibrium constant for association of degree

n

, component

i

K

Mij

chemical equilibrium constant for mixed association, components

i

and 

j

K

i

K

‐factor for component

i

(

K

i

 = 

y

i

/

x

i

)

l

membrane thickness

m

L

amount of liquid

mol, kg

m

arbitrary specific thermodynamic function

m

mass

kg

m

i

molality of component

i

mol/kg

partial molar property

mass flow

kg/s

M

molar mass

g/mol

moment of distribution function

Δ

m

, Δ

M

property change of mixing

n

number of components

n

number of data points

mole flow

mol/s

n

A

number of atoms in a molecule

N

A

Avogadro's number;

N

A

 = 6.023 · 10

23

N

th

number of theoretical stages

n

f

number of degrees of freedom

n

i

number of moles of component

i

mol

n

T

total number of moles

mol

N

total number of species

mol

Nu

Nußelt number

p

i

partial pressure of component

i

Pa

P

parachor

P

total pressure

Pa

P

i

permeability

kg/(s m Pa)

P

G

vapor pressure around a droplet

Pa

P

*

apparent permeability

kg/(s m

2

 Pa)

vapor pressure of component

i

Pa

Poy

i

Poynting factor of component

i

Pr

Prandtl number

q

i

relative van der Waals surface area of component

i

q

charge

C

q

vapor fraction

q

specific heat

J/mol, J/kg

specific heat flux

W/mol, W/kg

Q

heat

J

heat flow

W

Q

k

relative van der Waals surface area of group

k

r

i

relative van der Waals volume of component

i

r

i

ionic radius

r

i

segment number

r

ij

distance between two ions

i

and

j

m

R

universal gas constant;

R

 = 8.314471 J/mol K   = 1.98721 cal/mol K

Re

Reynolds number

R

k

relative van der Waals volume of group k

s

specific entropy

J/(mol K), J/(kg K)

s

abs

absolute specific entropy

J/(mol K), J/(kg K)

Δ

s

id

specific entropy of mixing

J/(mol K), J/(kg K)

standard entropy of reaction

J/(mol K), J/(kg K)

S

entropy

J/K

S

12

selectivity

T

absolute temperature

K

u

specific internal energy

J/mol, J/kg

Δ

u

ij

interaction parameter of the NRTL equation

K

u

internal energy

J

V

amount of vapor

mol, kg

v

specific volume

m

3

/mol, m

3

/kg

v*

characteristic volume

m

3

/mol

V

volume

m

3

V

i

volume fraction/mole fraction of component

i

(UNIQUAC, UNIFAC)

w

specific work

J/mol, J/kg

w

velocity

m/s

w*

speed of sound

m/s

W

t

technical work

J

w

t

specific technical work

J/mol, J/kg

w

weighting factor in objective functions

W(r)

distribution function

w

i

weighting factor of data point

i

w

i

weight fraction of component

i

x

i

mole fraction of component

i

in the liquid phase